Science and Mathematics Education Commons^™

Modeling Aircraft Takeoffs, Catherine Cavagnaro

CODEE Journal

Real-world applications can demonstrate how mathematical models describe and provide insight into familiar physical systems. In this paper, we apply techniques from a first-semester differential equations course that shed light on a problem from aviation. In particular, we construct several differential equations that model the distance that an aircraft requires to become airborne. A popular thumb rule that pilots have used for decades appears to emanate from one of these models. We will see that this rule does not follow from a representative model and suggest a better method of ensuring safety during takeoff. Aircraft safety is definitely a matter …

Odes And Mandatory Voting, Christoph Borgers, Natasa Dragovic, Anna Haensch, Arkadz Kirshtein, Lilla Orr

CODEE Journal

This paper presents mathematics relevant to the question whether voting should be mandatory. Assuming a static distribution of voters’ political beliefs, we model how politicians might adjust their positions to raise their share of the vote. Various scenarios can be explored using our app at https: //centrism.streamlit.app/. Abstentions are found to have great impact on the dynamics of candidates, and in particular to introduce the possibility of discontinuous jumps in optimal candidate positions. This is an unusual application of ODEs. We hope that it might help engage some students who may find it harder to connect with the more customary …

Solar Panels, Euler’S Method And Community-Based Projects: Connecting Differential Equations With Climate Change, Victor J. Donnay

CODEE Journal

How does mathematics connect with the search for solutions to the climate emergency? One simple connection, which can be explored in an introductory differential equations course, can be found by analyzing the energy generated by solar panels or wind turbines. The power generated by these devices is typically recorded at standard time intervals producing a data set which gives a discrete approximation to the power function $P(t)$. Using numerical techniques such as Euler’s method, one can determine the energy generated. Here we describe how we introduce the topic of solar power, apply Euler’s method to determine the energy generated, and …

Educators’ Beliefs About Using Academic Acceleration With Gifted Math Students And Others: Barriers And Opportunities, Jason Gorgia

Theses, Dissertations and Capstones

This study examined the perceptions of educators (i.e., math teachers, administrators, and others) for insight into the absence of acceleration as a common pedagogical strategy in mathematics, despite longstanding research supporting the practice for students gifted in math and the interest frequently articulated by policymakers and educators in boosting American K-12 students’ math achievement. Educators from 48 states responded to scale-based and open-ended questions about math acceleration through an online survey where 713 of 818 respondents were teachers, balanced almost evenly among elementary, middle, and high schools, and among urban, suburban, and rural settings. The responses of teachers and non-teaching …

Exploring The Role Of Undergraduate And Graduate Real Analysis Experiences In The Mathematical Trajectories Of Women Mathematicians From Historically Disenfranchised Groups, Te'a Riley

Mathematics Dissertations

This phenomenological study examines the role of undergraduate and graduate Real Analysis courses in shaping the mathematical trajectories of seven women Ph.D. mathematicians from groups historically disenfranchised in mathematics.Qualitative analysis of interviews explores various aspects of their development as mathematicians with a focus on their experiences in Real Analysis. This study applies Ryan & Deci’s (1985) Self-Determination Theory's Basic Psychological Need Theory and Critical Race Theory to analyze the trajectories of the participants. The research explores how the fulfillment of basic psychological needs in their Real Analysis courses may have influenced their academic and professional journeys. The basic psychological need …

Mapping With The Land: Co-Developing A Cumulative Impact Monitoring And Land Stewardship Framework With Sambaa K’E First Nation, Northwest Territories, Canada, Michael S. Mcphee

Theses and Dissertations (Comprehensive)

Across the Northwest Territories (NWT), Canada, Indigenous populations are striving to achieve effective environmental protection, whilst navigating complex methods, policies, and research relationships within co-management contexts. This thesis seeks to identify how differing cultural systems, environmental change, and fractured partnerships may be unified to align with the needs of the Sambaa K’e First Nation (SKFN), a remote Dehcho Dene community. Indigenous methodologies guided co-development of research questions with SKFN leadership which yielded objectives a) develop a GIS-based method to manage, organize and mobilize cultural and environmental data; b) develop a new stewardship monitoring procedure so that users can apply the …

Student Performance In Modern Physics In An Active, Partially-Flipped Classroom, Scott Yarbrough

Physics Dissertations

The effectiveness of the flipped classroom and hybrid-flipped (partially flipped, partially lecture-based) method of instruction has been extensively studied for high school and introductory undergraduate physics courses, and it has been shown to increase student understanding and performance. However, few studies have been done for upper-level undergraduate courses, and even fewer have been done for virtual courses. In Spring 2021 and Fall 2023, a fully virtual, hybrid-flipped Modern Physics course was taught, primarily to a class of primarily juniors and seniors, with some sophomores. All were STEM majors. The same course, with a similar enrolment and demographic of students, was …

Critical Convergence: Mapping The Boundaries Of How Faculty Interrogate Whiteness In The Geoscience Educational Landscape, James E. Hobbs

Educational Leadership & Policy Studies Dissertations

This study examined the role of faculty members in interrogating whiteness within geoscience education. The dominant reliance on whiteness as the primary way of knowing in geoscience education has long perpetuated a singular perspective that serves as a mechanism for reinforcing existing power structures rooted in white supremacy. Drawing on tenets from Critical whiteness Studies, Curriculum Theory, and Transformative Learning Theory, this research investigated U.S. higher education faculty members' strategies and challenges in disrupting whiteness within the geoscience curriculum.

Through critical qualitative narrative inquiry, data were collected through semi-structured interviews with geoscience faculty members across multiple institutions across the United …

Coalescence: A Carnivore Coexistence Curriculum That Braids Indigenous & Western Ecological Knowledge Into A Relevant And Experiential Learning Opportunity For Youth, Stephanie Anne Barron

Graduate Student Theses, Dissertations, & Professional Papers

As grizzly bears (Ursus arctos horriblis) begin to reoccupy more of their historic range, and as humans and large carnivore populations continue to increase, incidences of human carnivore conflict are on the rise. A decolonial curriculum designed in collaboration with the Confederated Salish and Kootenai Tribe’s wildlife biologists stands to increase awareness of Indigenous ecological knowledge and teach youth about the importance of coexistence with carnivores. Additionally, this project could greatly influence youth perceptions of grizzly bears and other large carnivores. This research project examines the development and implementation of a carnivore coexistence curriculum for youth that is guided by …

An Exploration Of Misconceptions In Introductory Physics, Christopher Mattthew Wheatley

Graduate Theses, Dissertations, and Problem Reports

The study of student misconceptions about physics concepts has long been an important area of inquiry in physics education research (PER). The research discussed in this dissertation builds upon the developments in PER by exploring the prevalence of consistently held undergraduate student misconceptions in introductory calculus-based physics. This thesis explores the nature of student misconceptions, mistakes, and naive answering patterns in both introductory undergraduate Newtonian mechanics and electromagnetism by applying a network analytic technique called module analysis to student responses to different concept inventories from institutions of various levels of incoming physics preparation. Each study applying these methods also demonstrates …

Analyzing A Smartphone Battle Using Bass Competition Model, Maila Hallare, Alireza Hosseinkhan, Hasala Senpathy K. Gallolu Kankanamalage

CODEE Journal

Many examples of 2x2 nonlinear systems in a first-course in ODE or a mathematical modeling class come from physics or biology. We present an example that comes from the business or management sciences, namely, the Bass diffusion model. We believe that students will appreciate this model because it does not require a lot of background material and it is used to analyze sales data and serve as a guide in pricing decisions for a single product. In this project, we create a 2x2 ODE system that is inspired by the Bass diffusion model; we call the resulting system the Bass …

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

How To Intercept A High-Speed Rocket With A Pair Of Compasses And A Straightedge?, Yagub N. Aliyev

CODEE Journal

In this paper a nonlinear differential equation arising from an elementary geometry problem is discussed. This geometry problem was inspired by one of the proofs of the first remarkable limit discussed in a typical first semester undergraduate Calculus course. It is known that the involved differential equation can be reduced to Abel’s differential equation of the first kind. In this paper the problem was solved using an approximate geometric method which constructs a piecewise linear solution approximation for the curve. The compass tool of GeoGebra was extensively used for these constructions. At the end of the paper, some generalizations are …

Centering Equity In Stem Teaching: Stem Ideas That Change The World, Ileana Vasu

Feminist Pedagogy

No discussion on equity/inequity makes sense without bringing power into that discussion. As instructors we need to ask questions such as “who decides and controls what knowledge is”, “whose identities are empowered and whose are erased”, “who has access and opportunity and who doesn’t”. Traditional teaching in STEM, including mathematics, assumes knowledge is objective, transmittable, repeatable to everyone. When educators follow a traditional curriculum, just like their teachers before them, they do so thinking their methods ensure equality and objectivity. These practices not only deny the role that Western patriarchal cultures have played in creating these so-called equitable practices, but …

Building Community, Competency, And Creativity In Calculus 2: Summary Of A Pilot Year Of Project Implementation, Jennifer Beichman, Candice R. Price

Feminist Pedagogy

In light of the COVID-19 pandemic, instructional modes at our institution moved to fully online and remote, then fully online but on campus, and back to in-person learning in fall 2021. To combat perceived issues in student engagement, we piloted using group projects in place of exams at the natural content break points in Calculus 2.

Southern Rio Grande Rift Kinematics And Geochronology, Big Bend Fold Geometry, And The Use Of Real Data In Geoscience Education: Contributions To The Understanding Of Big Bend Geology And To Public Geoscientific Literacy, Jessica Kelsch

Open Access Theses & Dissertations

The Big Bend region of Trans-Pecos Texas preserves a rich record of Rio Grande rifting and Laramide-age contraction that provide intrigue to national and state park visitors and field trips for undergraduate geology students. Despite its well-exposed geologic record, the Big Bend region remains an underutilized natural laboratory for studying these two tectonic events. This dissertation combines structural studies of Rio Grande rift and Laramide structures with public outreach and geoscience education studies focused on the Big Bend region. In Chapter 2, existing extensional-kinematic studies from parts of this region are compiled with new fault kinematic and U-Pb geochronologic data …

(R2054) Convergence Of Lagrange-Hermite Interpolation Using Non-Uniform Nodes On The Unit Circle, Swarnima Bahadur, Sameera Iqram, Varun .

Applications and Applied Mathematics: An International Journal (AAM)

In this research article, we brought into consideration the set of non-uniformly distributed nodes on the unit circle to investigate a Lagrange-Hermite interpolation problem. These nodes are obtained by projecting vertically the zeros of Jacobi polynomial onto the unit circle along with the boundary points of the unit circle on the real line. Explicitly representing the interpolatory polynomial as well as establishment of convergence theorem are the key highlights of this manuscript. The result proved are of interest to approximation theory.

The Underrepresentation Of Black Females In Cybersecurity, Makendra Latrice Crosby

Cybersecurity Undergraduate Research Showcase

The significance of cybersecurity methods, strategies, and programs in protecting computers and electronic devices is crucial throughout the technological infrastructure. Despite the considerable growth in the cybersecurity field and its expansive workforce, there exists a notable underrepresentation, specifically among Black/African American females. This study examines the barriers hindering the inclusion of Black women in the cybersecurity workforce such as socioeconomic factors, limited educational access, biases, and workplace culture. The urgency of addressing these challenges calls for solutions such as education programs, mentorship initiatives, creating inclusive workplace environments, and promoting advocacy and increased awareness within the cybersecurity field. Additionally, this paper …

Population Growth Models: Relationship Between Sustainable Fishing And Making A Profit, James Sandefur

CODEE Journal

In this paper, we develop differential equations that model the sustainable harvesting of species having different characteristics. Specifically, we assume the species satisfies one of two different types of density dependence. From these equations, we consider maximizing sustainable harvests. We then introduce a cost function for fishing and study how maximizing profit affects the harvesting strategy. We finally introduce the concept of open access which helps explain the collapse of many fish stocks.

The equations studied involve relatively simple rational and exponential functions. We analyze the differential equations using phase-line analysis as well as graphing approximate solutions using Euler's method, …

Scicomm To The Rescue, Becky Sanft, Angel Kaur, Evan Couzo, Sally Wasileski, Jessica Pisano

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Modeling Framework For Minimizing Spread Of Mathematics Anxiety In College Students, Sara Sony, Majid Bani-Yaghoub

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modelling Impact Of Diverse Vegetation On Crop-Pollinator Interactions, Morgan N. Beetler

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Correlation Between Scores On The Assessment And Learning In Knowledge Spaces Placement, Preparation, And Learning Test And General Chemistry Course Outcomes For Undergraduate Students At A Public Midsize Master's University, Crystal Kaye Keso

All NMU Master's Theses

This study examined the problem of gateway courses in Science, Technology, Engineering, and Mathematics (STEM), specifically, high-enrollment introductory chemistry courses with high rates of D, F, withdrawal, or incomplete grades. Previous research revealed a correlation between students’ prior mathematics knowledge and introductory chemistry course outcomes. Reports using the Assessment and Learning in Knowledge Spaces Placement, Preparation, and Learning (ALEKS PPL) test were limited in number. This study conducted a non-experimental retrospective correlational analysis between undergraduate students’ ALEKS PPL test scores and introductory chemistry course grades. The study’s theoretical framework was grounded in prerequisite and placement testing theories. The major findings …

Fibonacci Differential Equation And Associated Spiral Curves, Mehmet Pakdemirli

CODEE Journal

The Fibonacci differential equation is defined with analogy from the Fibonacci difference equation. The linear second order differential equation is solved for suitable initial conditions. The solutions constitute spirals in the polar coordinates. The properties of the spirals with respect to the Fibonacci numbers and the differences between the new spirals and classical spirals are discussed.

A Generalized Solution Method To Undamped Constant-Coefficient Second-Order Odes Using Laplace Transforms And Fourier Series, Laurie A. Florio, Ryan D. Hanc

CODEE Journal

A generalized method for solving an undamped second order, linear ordinary differential equation with constant coefficients is presented where the non-homogeneous term of the differential equation is represented by Fourier series and a solution is found through Laplace transforms. This method makes use of a particular partial fraction expansion form for finding the inverse Laplace transform. If a non-homogeneous function meets certain criteria for a Fourier series representation, then this technique can be used as a more automated means to solve the differential equation as transforms for specific functions need not be determined. The combined use of the Fourier series …

Exploring Retrieval Difficulties And Self-Confidence In An Assessment Of General Chemistry Students, Karen Julian, Morgan Balabanoff

The Cardinal Edge

Developing self-assessment skills is an important aspect of learning. Framed by assessment developed for the year-long sequence of general chemistry, students were asked to rate their ability to answer conceptual questions. Using cognitive interviews, this study revealed that people rely on a range of characteristics other than content knowledge to assess their confidence, including doubt, retrieval difficulty, and test-taking methods. These findings imply that more explicit instruction may be required to encourage correct self-assessment. Students can develop their metacognitive skills and calibrate their perceived ability by completing examinations meant to emphasize content knowledge gaps.

B/Lv Laboratory Accessibility Technology Adapted For Neurodiverse Chemistry Students, Christin B. Monroe

Journal of Science Education for Students with Disabilities

Text-to-speech technology is a common accommodation available for students with disabilities. Despite the ubiquitous nature of text-to-speech, this technology has not been explored in laboratory settings for neurodiverse college students. This study explores the adaptability of laboratory accessible text-to-speech technology (originally developed for blind/low vision (B/LV) students) for neurodiverse students. Students were asked to provide general feedback about the usability and effectiveness of the technology using Likert surveys. The students also answered open-ended questions about how the technology could be adapted to be more neurodiverse friendly. Overall, more than 50% of the students found the technology useful but had specific …

The Value Of Stem As An Educational Tool For Enhancing Cognitive Development, Alessandra Olmedo Robles, Leaders 20/20

San Diego Regional Climate Collaborative

STEM is an acronym for Science, Technology, Engineering, and Math. The focus of STEM education is to provide a holistic approach through hands-on, problem-based learning where students are able to take what they learn in the classroom and apply it to real world problems.

Undetermined Coefficients With Hyperbolic Sines And Cosines, Laurie A. Florio, George L. Fischer

CODEE Journal

The method of undetermined coefficients is commonly applied to solve linear, constant coefficient, non-homogeneous ordinary differential equations when the forcing function is from a selected class of functions. Often the hyperbolic sine and cosine functions are not explicitly included in this list of functions. Through a set of guided examples, this work argues that the hyperbolic sine and cosine ought to be included in the select class of functions. Careful explanation is provided for the necessary treatment of the cases where the argument of the hyperbolic sine and/or cosine functions matches one or both of the roots of the characteristic …

Synesthesia: 3.1415... Orange.Whiteperiwinklewhiteblue..., Shelly Sheats Harkness, Bethany A. Noblitt, Nicole Giesbers

Journal of Humanistic Mathematics

In this paper we address the questions: What is synesthesia? What support(s) can teachers provide for their students who have synesthesia? Nicole, a future mathematics teacher who possesses this synesthesia “superpower”, describes how it impacted her learning. We collected data for this case study through an audio-recorded and transcribed interview, as well as from subsequent email correspondence between the three authors. We asked Nicole three kinds of questions: questions she is frequently asked, questions she would like to be asked, and questions teachers (like Shelly and Beth) might ask. Results indicate that synesthesia may have helped Nicole learn English as …